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#include "convex.h"
double slope(point_t *P, point_t *Q) {
return (Q->y - P->y) / ((double)(Q->x) - (double)(P->x));
}
double *get_convex_minorant(uint64_t n, double *Gammas) {
if (n < 2) {
return Gammas;
}
list_t *L = (list_t *)calloc(1, sizeof(list_t));
L->p = (point_t *)calloc(1, sizeof(point_t));
L->p->x = 0;
L->p->y = Gammas[0];
list_t *pos = L;
for (uint64_t i = 1; i < n; i++) {
pos->next = (list_t *)calloc(1, sizeof(list_t));
pos->next->p = (point_t *)calloc(1, sizeof(point_t));
pos->next->p->x = i;
pos->next->p->y = Gammas[i];
pos->next->prev = pos;
pos = pos->next;
}
pos->next = (list_t *)calloc(1, sizeof(list_t));
pos->next->p = (point_t *)calloc(1, sizeof(point_t));
pos->next->p->x = n;
pos->next->p->y = 0;
pos->next->prev = pos;
list_t *X = L;
list_t *Y = L->next;
list_t *Z = Y->next;
while (true) {
if (slope(X->p, Y->p) <= slope(Y->p, Z->p)) {
X = Y;
Y = Z;
if (Z->next == NULL) {
break;
} else {
Z = Z->next;
}
} else {
Y->prev->next = Y->next;
Y->next->prev = Y->prev;
free(Y->p);
free(Y);
if (X->prev != NULL) {
Y = X;
X = X->prev;
} else {
if (Z->next != NULL) {
Y = Z;
Z = Z->next;
} else {
break;
}
}
}
}
pos = L;
double *g = (double *)calloc(n, sizeof(double));
double rho = 0;
for (uint64_t i = 0; i < n; i++) {
if (i > pos->next->p->x) {
pos = pos->next;
}
g[i] = pos->p->y + ((double)i - (double)(pos->p->x)) * (pos->next->p->y - pos->p->y) / ((double)(pos->next->p->x) - (double)(pos->p->x));
if (Gammas[i] - g[i] > rho) {
rho = Gammas[i] - g[i];
}
}
for (uint64_t i = 0; i < n; i++) {
g[i] += rho / 2;
}
while (L != NULL) {
free(L->p);
list_t *L_save = L;
L = L->next;
free(L);
}
return g;
}
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